NEW YORK — Republican presidential nominee Mitt Romney said Tuesday that he thinks teachers’ unions should be banned from making political contributions because union leaders often negotiate contracts with Democratic politicians they’ve helped elect, a situation he called “an extraordinary conflict of interest.”

“I believe that we simply can’t have a setting where the teachers’ unions are able to contribute tens of millions of dollars to the campaigns of politicians and then those politicians, when elected, stand across from them at the bargaining table, supposedly to represent the interest of the kids,” Romney told host Brian Williams in a 45-minute appearance at NBC’s Education Nation Summit in New York.

He said it is “a mistake” to allow unions to make such donations, which he argued represent “an extraordinary conflict of interest.”

“I think we’ve got to get the money out of the teachers’ unions going into campaigns,” he said. “It’s the wrong way for us to go. We have got to separate that.”

Romney contended that “the largest contributors to the Democratic Party are the teachers’ unions.” But a tally by the Center for Responsive Politics, which tracks campaign contributions, shows that the education industry is the third-largest contributor to President Barack Obama’s reelection campaign, behind retirees and those in the legal field.

A Romney spokeswoman clarified that the candidate was referring to the fact that the vast majority of donations made by the National Education Association benefit Democrats.

Romney’s argument against political donations by teachers’ unions appears to be at odds with the Supreme Court’s 2010 landmark Citizens United ruling, in which the court found that corporations and unions have a First Amendment right to spend unlimited amounts on campaigns.

Romney’s comments come one week after a Chicago teachers strike that pitted educators in the country’s third-largest school district against Mayor Rahm Emanuel, a Democrat, in a week-long standoff over teacher evaluations and other reforms.

In that showdown, the Romney campaign sought to align itself with Emanuel and Chicago parents rather than the unions. Asked Tuesday whether he would allow such strikes if he were president, Romney responded, “I don’t know that I would prevent teachers from being able to strike.”

In an interview with NBC’s Savannah Guthrie that aired ahead of Romney’s appearance, Obama also weighed in on the strike. He said that he is “glad it was resolved” but added that “from the perspective of Democrats, we can’t just sit on the status quo or say that money’s the only issue. Reform is important, also.”

“I think Governor Romney and a number of folks try to politicize the issue and do a lot of teacher-bashing,” Obama said when asked about Romney’s charge that the White House had sided with the unions in the battle. “When I meet teachers all across the country, they are so devoted, so dedicated to their kids. And what we’ve tried to do is actually break through this left-right, conservative-liberal gridlock. . . . You know, I just really get frustrated when I hear teacher-bashing as evidence of reform.”

Romney said in Tuesday’s interview that he thinks it’s preferable for one parent to stay home when children are young. The comment came during a discussion of early childhood education and preparing for kindergarten. “It’s an advantage to have two parents, but to have one parent to stay closely connected and at home during those early years of education can be very very important,” he said.

Romney’s wife, Ann, was a stay-at-home mother to the couple’s five sons.

In 2011, 63.9 percent of the mothers with children younger than 6 held jobs outside the home, according to the Bureau of Labor Statistics.